Bifurcations in the Regularized Ericksen Bar Model

M. Grinfeld, G. J. Lord

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider the regularized Ericksen model of an elastic bar on an elastic foundation on an interval with Dirichlet boundary conditions as a two-parameter bifurcation problem. We explore, using local bifurcation analysis and continuation methods, the structure of bifurcations from double zero eigenvalues. Our results provide evidence in support of Müller's conjecture (Müller, Calc. Var. 1:169-204, 1993) concerning the symmetry of local minimizers of the associated energy functional and describe in detail the structure of the primary branch connections that occur in this problem. We give a reformulation of Müller's conjecture and suggest two further conjectures based on the local analysis and numerical observations. We conclude by analysing a "loop" structure that characterizes (k,3k) bifurcations. © 2007 Springer Science+Business Media B.V.

Original languageEnglish
Pages (from-to)161-173
Number of pages13
JournalJournal of Elasticity
Volume90
Issue number2
DOIs
Publication statusPublished - Feb 2008

Keywords

  • Ericksen bar model
  • Lyapunov-Schmidt analysis
  • Microstructure

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